Thin film growth simulation with noise reduction techniques in (2+1) dimensional substrate systems

Abstract

Two noise reduction techniques: the long surface diffusion length noise reduction technique and multiple hit noise reduction technique are used to produce smooth film surface in thin film growth simulation. The long surface diffusion length technique is equivalent to the increase in growth temperature while the multiple hit technique is a computational technique. We have simulated thin film growth by using Das Sarma-Temborenea (DT) model with the two noise-reduction techniques in two-dimensional substrates to compare whether the multiple hit noise reduction technique is equivalent to the long surface diffusion length noise reduction technique. Our simulation results show that both techniques are equivalent for the study of layer-by-layer growth which is very smooth film surface growth indicated by oscillations in surface roughness during early growth time. Both techniques produce a smoother film surfaces. Additionally, we find that the damping time t[subscript c], the time when the layer-by-layer damps out, depends on the noise reduction parameters with power law relations: t[subscript c] ~(𝓁/L)[superscript δ] for the long surface diffusion length technique when is the substrate size, 𝓁 is surface diffusion length and δ = 1.5, and t[subscript c] ~m[superscript µ], for the multiple hit technique when m is multiple hit parameter and µ = 2.5. We also study effects of the two noise reduction techniques on the growth exponent β of the DT model in two-dimensions. Our results show that the growth exponent decreases as parameter 𝓁 and m are increased. At large m, the growth exponent converges to β ≈ 0.07 while at large 𝓁, the growth exponent fluctuates and around β ≈ 0.12-0.13. In addition, Finite size effects on the growth exponent and the roughness exponent of (2+1)-dimensional DT model are studied as well. We found that the growth exponent is not significantly affected by the substrate size while the roughness exponent is affected greatly. Extrapolation technique shows that the roughness exponent decreases to α ≈ 0.005 when the substrate size approaches L→∞.